To solve this problem, you can use the direct variation equation, which relates y and x when y varies directly as the square root of x. The equation can be written as:
y = k√x
Where k is the constant of variation.
Given that y = 28 when x = 16, you can use these values to find the value of k:
28 = k√16
Now, solve for k:
k√16 = 28
k * 4 = 28 (since √16 = 4)
k = 28 / 4
k = 7
Now that you have the value of k, you can use it to find x when y = 49:
49 = 7√x
To isolate x, divide both sides of the equation by 7:
√x = 49 / 7
√x = 7
Now, square both sides to solve for x:
x = (√7)^2
x = 7
So, when y = 49, x = 7.